overall mean
When ANOM is used with normal data, the overall mean is calculated as the average of all the data. Here is a simple example.
Factor level | Data | Cell mean
-------------|---------------------------------------------------
1 | 1 3 | 2
2 | 2 4 | 3
3 | 6 7 9 8 7 9 5 4 6 9 | 7
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ANOM calculates the overall mean as (1 + 3 +2 + 4 + 6 + 7 + 9 + 8 + 7 + 9 + 5 + 4 + 6 + 9) / 14 = 5.7.
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Note |
Analysis of variance calculates the overall mean as the average of the cell means. For the data above, analysis of variance calculates the overall mean as (2 + 3 + 7) / 3 = 4. The two methods give the same answer if the design is balanced, but they differ when the design is unbalanced. |
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